Geologists and geophysicists are interested in the characteristics of the formations encountered by a drill bit as it is drilling a well for the production of hydrocarbons from the earth. Such information is useful in determining the correctness of the geophysical data used to choose the drilling location and in choosing subsequent drilling locations. In horizontal drilling, such information can be useful in determining the location of the drill bit and the direction that drilling should follow.
Such information can be derived in a number of ways. For example, cuttings from the mud returned from the drill bit location can be analyzed or a core can be bored along the entire length of the borehole. Alternatively, the drill bit can be withdrawn from the borehole and a "wireline logging tool" can be lowered into the borehole to take measurements. In still another approach, "measurement while drilling" ("MWD") or "logging while drilling" ("LWD") tools make measurements in the borehole while the drill bit is working. There are a wide variety of logging tools, including resistivity tools, density tools, sonic or acoustic tools, and imaging tools.
A density tool 10 may be part of a drill string 12 that is used to drill a borehole 14 through a formation 16, as illustrated in FIG. 1. The drill string 12 is not horizontal but instead is, at least for the portion of the borehole shown in FIG. 1, drilled at an angle. Consequently, the drill string 12 and density tool 10 tend to be closer to one side of the borehole 14 than to the other, such that the distance d is smaller than the distance D. Further, the borehole 14 changes in diameter along its length due to cave-ins and the like, such that the distance E is larger than the distance D. Drilling mud is pumped down the drill string 12 through channel 18 to the bit (not shown) where it is circulated back to the surface through the annulus 20 between the drill string 12 and the formation 16.
The density tool includes a source 22 of gamma rays, preferably a cesium 137 source. Gamma rays from the source are emitted into the formation 16 through a low density window 24 as the drill string 12 rotates. A near detector 26 detects the gamma rays when they escape from the formation 16 and pass through a near detector low density window 28. The intensity of the escaping gamma rays is attenuated as they travel through the formation. For high energy gamma rays, the attenuation is caused by Compton scattering. For lower energy gamma rays, the attenuation is caused by photoelectric absorption. In the latter case, the attenuation is characterized by the photoelectric factor, or P.sub.e.
A far detector 30 detects the attenuated gamma rays when they escape from the formation 16 and pass through a far detector low density window 32. The low density windows 24, 28 and 32 protrude through a stabilizer 34. The attenuation of the gamma rays is related to the electron density of the formation 16, which is, in turn, related to the common density of the formation 16. The near detector's response is influenced by borehole effects, which include effects related to the size of the borehole. The combined response of the near and far detector is used to provide an indication of the density of the formation.
It is useful to know the size of the borehole for a variety of reasons. For example, knowledge of the borehole size allows a computation of the volume of annulus which must be filled with cement when a casing is inserted into the borehole and secured with cement. The borehole size can also be a factor in the computation of some geological characteristics of the formation. Further, knowledge of borehole size can be a quality check on the results of other measurements that are affected by the borehole size.
In some wireline applications, borehole size is measured by a caliper, which is an arm that reaches out from the wireline tool and touches the side of the borehole. The caliper determines borehole size from the distance the arm has to reach to touch the side of the borehole. Borehole size can also be measured acoustically.